The document discusses scale drawings and transformations. It defines scale as the ratio of the size of the drawing to the actual object. Scale drawings use different units of measurement for length and area. To find distances and scales, formulas use the ratio of the image to object. Enlargements increase the size of the drawing by a scale factor, with the area of the image equal to the scale factor squared times the area of the object. Transformations can be used to determine if shapes are similar and to solve problems involving scales, distances, areas, and volumes using ratios and formulas.

1. Mathematics Form 3 – Chapter 9 & 10 © Notes Prepared by Kelvin
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Form 3 - Chapter 9 – Scale Drawing [Notes Completely]
1. Ratio Scale of Scale Drawing = size of drawing(image) : size of actual object
2. Scale Drawing= Length of a side of the drawing .
Length of the corresponding side of the object
3. **1 : __. eg. 1 : 2, 1 : 2
1
.
4. Use in map.
5. Unit conversation:
1km=1000m,1m=100cm,. 1cm=10mm.
6. Unit conversation (in area): 1km2
=1 000 000 m2
,
1m2
=1 00 00 cm2
, 1cm2
=1 0 0 mm2
.
7. Solving problems (formula): FINDING
DISTACE: O
I
O
I
 , FINDING SCALE: I:O.
8. Redraw on the grid dependon scale.

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4.
Solve the following problems.
The length of a roomis 3.5 cm on a map
drawn to a scale of 1:200. Find the
length, in m, of the room.
A road with a length 70 km is represented
by 3.5 cm on a map. Find the scale of the
map.
Square B with 256 cm2
is the scale
drawing same as square A with 64
cm2
. Find the scale used.
The diagram shows a solid in the
shape of a cone with a
hemisphere at the top,drawn to a
scale of 1:5. Find the actual
volume of the solid.
(Use= )

5. Mathematics Form 3 – Chapter 9 & 10 © Notes Prepared by Kelvin
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Form 3 - Chapter 10 – Transformation II [Notes Completely]
1. Topic same as Form3 - Chapter9 (scale)
2. Similarity of Shapes (Yes and No)
3. Enlargement Scale = Length of (the side) the drawing .
Length of (the corresponding side) the object
4. Finding value: FIND : ORIGIN x = 5
. 8 10 (打岔乘)
10x=40
x = 10÷10
x = 4cm
5. Area of image = (scale factor)2
× area of object *k=scale factor
6. TriangularFormula:
I
k2 O
7. Complete the following table:
Scale factor Area of object (cm2
) Area of image (cm2
)
4 12
1.5 12
36 81
136 8.5

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6 (b)(i) (ii)

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9